CN113763916A - Nonlinear hybrid active noise control method and control system - Google Patents

Nonlinear hybrid active noise control method and control system Download PDF

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CN113763916A
CN113763916A CN202111041420.0A CN202111041420A CN113763916A CN 113763916 A CN113763916 A CN 113763916A CN 202111041420 A CN202111041420 A CN 202111041420A CN 113763916 A CN113763916 A CN 113763916A
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active noise
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CN113763916B (en
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程亚兵
张瑞
陈书明
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Jilin University
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    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10K—SOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
    • G10K11/00—Methods or devices for transmitting, conducting or directing sound in general; Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/16—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/175—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound
    • G10K11/178—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound by electro-acoustically regenerating the original acoustic waves in anti-phase
    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10K—SOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
    • G10K11/00—Methods or devices for transmitting, conducting or directing sound in general; Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/16—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/175—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound
    • G10K11/178—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound by electro-acoustically regenerating the original acoustic waves in anti-phase
    • G10K11/1781—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound by electro-acoustically regenerating the original acoustic waves in anti-phase characterised by the analysis of input or output signals, e.g. frequency range, modes, transfer functions
    • G10K11/17813—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound by electro-acoustically regenerating the original acoustic waves in anti-phase characterised by the analysis of input or output signals, e.g. frequency range, modes, transfer functions characterised by the analysis of the acoustic paths, e.g. estimating, calibrating or testing of transfer functions or cross-terms
    • G10K11/17815—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound by electro-acoustically regenerating the original acoustic waves in anti-phase characterised by the analysis of input or output signals, e.g. frequency range, modes, transfer functions characterised by the analysis of the acoustic paths, e.g. estimating, calibrating or testing of transfer functions or cross-terms between the reference signals and the error signals, i.e. primary path
    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10K—SOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
    • G10K11/00—Methods or devices for transmitting, conducting or directing sound in general; Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/16—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/175—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound
    • G10K11/178—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound by electro-acoustically regenerating the original acoustic waves in anti-phase
    • G10K11/1787—General system configurations
    • G10K11/17873—General system configurations using a reference signal without an error signal, e.g. pure feedforward

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Abstract

The invention belongs to the technical field of active noise control, and particularly relates to a nonlinear hybrid active noise control method and a nonlinear hybrid active noise control system. The control method comprises the steps of firstly, obtaining a narrow-band reference signal and a wide-band reference signal; secondly, carrying out nonlinear expansion and filtering on the broadband reference signal to obtain a final output signal of the broadband subsystem; carrying out nonlinear expansion and filtering on the narrowband reference signal to obtain a final output signal of the narrowband subsystem; fourthly, obtaining an output signal of the nonlinear hybrid active noise control system; fifthly, updating weight coefficients of feedforward filters in the broadband active noise reduction subsystem and the narrowband active noise reduction subsystem; the control system comprises a signal separation subsystem, a narrow-band active noise reduction subsystem, a wide-band active noise reduction subsystem, a computing system and an updating system; the invention can improve the nonlinear adaptive capacity of the algorithm and improve the noise reduction capacity of the broadband active noise reduction subsystem.

Description

Nonlinear hybrid active noise control method and control system
Technical Field
The invention belongs to the technical field of active noise control, and particularly relates to a nonlinear hybrid active noise control method and a nonlinear hybrid active noise control system.
Background
With the development of the industry, the noise of mechanical equipment is more and more emphasized, and particularly, the noise emitted by some rotating machines is composed of broadband and narrowband frequency components. To control this noise, many active noise control systems have been developed. The active noise control system is a new technology based on the principle of sound phase interference elimination, and comprises three devices of a reference microphone, a loudspeaker and an error microphone. With the development of high performance digital signal processing chips, active noise control techniques have become more feasible. Over the past several decades, a variety of broadband active noise control systems have been proposed that are unable to attenuate the noise generated by rotating machinery without the inclusion of a narrowband active noise reduction subsystem.
In industrial environments where the acoustic transmission path exhibits nonlinear characteristics, many nonlinear active noise control systems have been proposed. A function-linked artificial neural network (FLANN) filter is an effective structure to solve the non-linearity problem, and many other filters have been proposed and exhibit good attenuation performance, such as volterra filters, bilinear filters, kernel filters, and the like. Since the noise emitted from the rotating electric machine is composed of wide-band and narrow-band frequency components, the above-described filter still cannot suppress such a noise signal.
The traditional hybrid active noise control system consists of a signal separation subsystem, a narrow-band active noise reduction subsystem and a wide-band active noise reduction subsystem, and the active noise control system has good mixed noise suppression capability. However, in a non-linear environment, the performance of the conventional hybrid active noise control system is greatly reduced because the system has no non-linear part. An improved active noise control system, called a hybrid function-linked artificial neural network (HFLANN) system, is proposed, which adds a function-linked artificial neural network structure to a traditional hybrid active noise control system, and numerical simulation proves the effectiveness of the system. However, the wideband active noise reduction subsystem of the HFLANN algorithm system applies the FXLMS algorithm, which performs poorly in attenuating wideband noise. In addition, the narrow-band active noise reduction subsystem of the HFLANN algorithm has no function-linked artificial neural network structure to adapt to a nonlinear environment.
Disclosure of Invention
The invention provides a nonlinear hybrid active noise control method and a nonlinear hybrid active noise control system, wherein a signal separation subsystem is designed, a mixed signal is decomposed into a broadband signal and a narrowband signal, the broadband signal and the narrowband signal are subjected to nonlinear expansion, the expanded broadband signal is subjected to discrete wavelet transform and then input into the broadband active noise reduction subsystem for processing, the expanded narrowband signal is input into the narrowband active noise reduction subsystem for processing, and the processing results of the two subsystems are added to obtain an output signal of the nonlinear hybrid active noise control system. The invention can improve the nonlinear adaptability, improve the noise reduction capability of the broadband active noise reduction subsystem and solve the problems of the existing active noise control method.
The technical scheme of the invention is described as follows by combining the attached drawings:
a nonlinear hybrid active noise control method, comprising the steps of:
step one, acquiring a mixed reference signal required by a system, and separating a narrowband reference signal and a broadband reference signal in the mixed reference signal through a signal separation subsystem;
step two, carrying out nonlinear expansion on the broadband reference signal through a FLANN filter in the broadband active noise reduction subsystem to obtain a first broadband output signal, carrying out discrete wavelet transformation on the first broadband output signal to obtain a second broadband output signal, and inputting the second broadband output signal into a broadband feedforward filter to obtain a third broadband output signal, namely a final output signal of the broadband subsystem;
step three, carrying out nonlinear expansion on a narrow-band reference signal through a FLANN filter in a narrow-band active noise reduction subsystem to obtain a first narrow-band output signal, and inputting the first narrow-band output signal into a narrow-band feedforward filter to obtain a second narrow-band output signal, namely a final output signal of the narrow-band subsystem;
step four, summing the final output signal of the wide-band subsystem obtained in the step two and the final output signal of the narrow-band subsystem obtained in the step three through a computing system to obtain an output signal of the nonlinear hybrid active noise control system;
and step five, updating the weight coefficient of the feedforward filter in the broadband active noise reduction subsystem by the updating system by adopting an M-max selector, and updating the weight coefficient of the feedforward filter in the narrowband active noise reduction subsystem by adopting an FELMS algorithm, so as to obtain an optimal output signal of the nonlinear hybrid active noise control system.
The specific method of the first step is as follows:
the obtained mixed reference signal is x (n), and the narrow-band reference signal is ys(n) the broadband reference signal is xB(n); wherein, the narrowband reference signal ys(n) is:
Figure BDA0003249396250000031
in the formula, Q is the number of narrow-band frequencies;
Figure BDA0003249396250000032
and
Figure BDA0003249396250000033
discrete fourier coefficients for the signal separation subsystem; x is the number ofai(n) is the cosine component of the narrowband reference signal, xai(n)＝cos(ωin)，ωiAngular frequency that is a narrowband component in the reference signal; x is the number ofbi(n) is the sinusoidal component of the narrow-band reference signal, xbi(n)＝sin(ωin)，ωiAngular frequency that is a narrowband component in the reference signal;
wideband reference signal xB(n) is:
xB(n)＝x(n)-ys(n)。
the specific method of the second step is as follows:
21) the wideband reference signal xB(n) the first wideband output signal extended by the FLANN nonlinear filter is:
HB(n)
＝[xB(n)sin(πxB(n))cos(πxB(n))…sin(AπxB(n))cos(AπxB(n))…x(n
-1)sin(πxB(n-1))cos(πxB(n
-1))…sin(AπxB(n-1))cos(AπxB(n-1))…xB(n-N
+1)sin(πxB(n-N+1))cos(πxB(n-N
+1))…sin(AπxB(n-N+1))cos(AπxB(n-N+1))]
in the formula, xB(n) is a wideband reference signal; a is the order of the broadband active noise reduction subsystem reference signal expanded by the FLANN function; n is the length of the feedforward filter;
22) said first broadband output signal HB(n) performing a discrete wavelet transform to obtain:
Figure BDA0003249396250000041
in the formula, Ψj,k(n) is a discretized wavelet function;
Figure BDA0003249396250000042
j is a discrete scale factor; k is a discrete shift factor; z is a rational number set; n is the length of the feedforward filter; Ψ (2)-jn-k) a wavelet function;
the second broadband output signal after discrete wavelet transform reconstruction is:
Figure BDA0003249396250000043
wherein j is a discrete scale factor; k is a discrete shift factor; w (2)-j,2-jk) Is a discrete wavelet coefficient; Ψ (2)-jn-k) is a wavelet function;
23) the final output signal of the wide-band subsystem obtained by inputting the second wide-band output signal into the wide-band feedforward filter is as follows:
Figure BDA0003249396250000044
wherein n is a time index; w is ai(n) is the filter weight coefficient of the broadband active noise reduction subsystem; u. ofi(n) is a signal obtained by expanding a reference signal of the broadband active noise reduction subsystem; a is broadband masterThe order of the reference signal of the dynamic noise reduction subsystem after being extended by a FLANN function; k is the number of layers of the signal after function expansion after discrete wavelet transform; i is the signal order after discrete wavelet transform; (2P +1) (k +1) is the number of frequency bands obtained by the input signals of the broadband active noise reduction subsystem after FLANN function expansion and discrete wavelet transformation.
The concrete method of the third step is as follows:
31) the narrowband reference signal ys(n) the first narrowband output signal extended by the FLANN nonlinear filter is:
Hai(n)
＝[xai(n)sin(πxai(n))cos(πxai(n))…sin(Pπxai(n))cos(Pπxai(n))…xai(n
-1)sin(πxai(n-1))cos(πxai(n
-1))…sin(Pπxai(n-1))cos(Pπxai(n-1))…xai(n-N
+1)sin(πxai(n-N+1))cos(πxai(n-N
+1))…sin(Pπxai(n-N+1))cos(Pπxai(n-N+1))]
Hbi
＝[xbi(n)sin(πxbi(n))cos(πxbi(n))…sin(Pπxbi(n))cos(Pπxbi(n))…xbi(n
-1)sin(πxbi(n-1))cos(πxbi(n
-1))…sin(Pπxbi(n-1))cos(Pπxbi(n-1))…xbi(n-N
+1)sin(πxbi(n-N+1))cos(πxbi(n-N
+1))…sin(Pπxbi(n-N+1))cos(Pπxbi(n-N+1))]
in the formula, Hai(n) is a narrowband reference signal cosine component FLANN extension; hbiCarrying out FLANN expansion on a narrow-band reference signal sinusoidal component; x is the number ofai(n) is the narrowband reference signal cosine component; x is the number ofbi(n) is a narrow-band reference signal sine componentAn amount; p is the order of the narrow-band signal expanded by the FLANN function; n is the length of the feedforward filter;
32) the final output signal of the narrowband subsystem obtained by inputting the first narrowband outgoing signal into the narrowband feedforward filter is as follows:
Figure BDA0003249396250000051
wherein n is a time index;
Figure BDA0003249396250000052
the filter weight coefficients of the n moments narrow-band active noise reduction subsystem are respectively; x is the number ofNai(n) is a signal of a reference signal cosine component of the narrow-band active noise reduction subsystem at the moment n after FLANN expansion; x is the number ofNbi(n) is a signal of a sinusoidal component of a reference signal of the narrowband active noise reduction subsystem at n moments after FLANN expansion; q is the number of angular frequencies of the narrow-band component; and P is the order of the narrowband signal after being extended by the FLANN function.
The output signal of the nonlinear hybrid active noise control system in the fourth step is specifically:
y(n)＝yB(n)+yN(n)
in the formula, yB(n) is the final output signal of the broadband subsystem; y isNAnd (n) is a narrow-band output signal.
The concrete method of the fifth step is as follows:
updating the weight coefficient of a filter in the broadband active noise reduction subsystem by adopting an M-max selector, and realizing the following steps:
wi(n+1)＝wi(n)+μBe(n)mi(n)
in the formula, wi(n) is the weight coefficient of the filter of the broadband active noise reduction subsystem; i is the order of the broadband signal; mu.sBStep size factor of the broadband active noise reduction subsystem; e (n) is the total error signal of the system; m isi(n) is the filtered wideband reference signal after selection by the M-max selector;
updating the weight coefficient of a filter in the narrow-band active noise reduction subsystem by using an FELMS algorithm, and realizing the following steps:
Figure BDA0003249396250000061
Figure BDA0003249396250000062
in the formula (I), the compound is shown in the specification,
Figure BDA0003249396250000063
the filter weight coefficients of the n moments narrow-band active noise reduction subsystem are respectively; mu.sNStep size factor for the narrowband active noise reduction subsystem;
Figure BDA0003249396250000064
to estimate the secondary acoustic path length; e.g. of the typef(n) is the filtered error signal;
Figure BDA0003249396250000065
to be delayed
Figure BDA0003249396250000066
Counting the number of narrowband reference signals;
Figure BDA0003249396250000067
to estimate a secondary acoustic path;
the total error signal e (n) is:
e(n)＝d(n)-y′(n)
wherein d (n) is a nonlinear primary acoustic channel model with a relationship between output and reference signal input of d (n) ═ x (n) +0.8x (n-1) +0.3x (n-2) +0.4x (n-3) -0.8x (n) x (n-1) +0.9x (n) x (n-2) +0.7x (n) x (n-3) -3.9x (n-2) + n)2(n-1)x(n-2)-2.6x2(n- 1)x(n-3)+2.1x2(n-2) x (n-3), y '(n) is the output signal after the total output signal y (n) has passed through the secondary path, y' (n) ═ y (n) × s (n), and s (n) is the secondary acoustic path.
A nonlinear hybrid active noise control system is used for realizing a nonlinear hybrid active noise control method and comprises a signal separation subsystem, a narrow-band active noise reduction subsystem, a broadband active noise reduction subsystem, a computing system and an updating system;
the signal separation subsystem is used for separating a narrowband reference signal and a wideband reference signal from a mixed reference signal;
the broadband active noise reduction subsystem is used for expanding and filtering a broadband reference signal to obtain a broadband output signal;
the narrowband active noise reduction subsystem is used for expanding and filtering a narrowband reference signal to obtain a narrowband output signal;
the computing system is used for summing the broadband output signal and the narrowband output signal to obtain an output signal of the nonlinear hybrid active noise control system;
the updating system is used for updating the weight coefficient of the feedforward filter in the broadband active noise reduction subsystem and the weight coefficient of the feedforward filter in the narrowband active noise reduction subsystem.
The invention has the beneficial effects that:
1) compared with the traditional hybrid control method, the nonlinear hybrid active noise control method and the control system have the advantages that the nonlinear path of the sound transmission process is considered, most sound wave transmission environments can be adapted, and a better noise reduction effect is realized; the discrete wavelet transform is added in the broadband active noise reduction subsystem, so that the noise reduction effect of the broadband active noise reduction subsystem can be effectively optimized;
2) according to the nonlinear hybrid active noise control method and the nonlinear hybrid active noise control system, a simplified algorithm is adopted in the process of updating the weight coefficient, an M-max selector is adopted in the process of updating the weight coefficient of the broadband active noise reduction subsystem, and the number of the weight coefficients in the updating process is reduced; in the process of updating the weight coefficient of the narrow-band active noise reduction subsystem, the FELMS algorithm is adopted, so that the computational complexity of updating the weight coefficient of the multi-frequency narrow-band active noise reduction subsystem is effectively reduced.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
FIG. 1 is a schematic block diagram of a nonlinear hybrid active noise control method according to the present invention;
FIG. 2 is a schematic block diagram of an improved hybrid function-linked artificial neural network (IHFLANN) algorithm used in the comparative experiment of the present invention;
FIG. 3 is a functional block diagram of a FLANN nonlinear filter according to the present invention;
FIG. 4a is a graph of the amplitude frequency response of a secondary acoustic path used in comparative experiments with the present invention;
FIG. 4b is a graph of the phase frequency response of the secondary acoustic path used in comparative experiments of the present invention;
FIG. 5 is a graph of the average noise reduction of various active noise control algorithms with white Gaussian noise and complex sinusoidal noise as wide-band and narrow-band mixed reference signals;
FIG. 6 is a graph of the average noise reduction of various active noise control algorithms with pink noise and composite sinusoidal noise as wide-band and narrow-band mixed reference signals;
fig. 7 is a graph of the average noise reduction of various active noise control algorithms with Henon noise and composite sinusoidal noise as wide-narrow band mixed reference signals.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting of the invention. It should be further noted that, for the convenience of description, only some of the structures related to the present invention are shown in the drawings, not all of the structures.
Referring to fig. 1 and 3, a nonlinear hybrid active noise control method includes the following steps:
step one, acquiring a mixed reference signal required by a system, and separating a narrowband reference signal and a broadband reference signal in the mixed reference signal through a signal separation subsystem;
the obtained mixed reference signal is x (n), and the narrow-band reference signal is ys(n) the broadband reference signal is xB(n); wherein, the narrowband reference signal ys(n) is:
Figure BDA0003249396250000081
in the formula, Q is the number of narrow-band frequencies;
Figure BDA0003249396250000091
and
Figure BDA0003249396250000092
discrete fourier coefficients for the signal separation subsystem; x is the number ofai(n) is the cosine component of the narrowband reference signal, xai(n)＝cos(ωin)，ωiAngular frequency that is a narrowband component in the reference signal; x is the number ofbi(n) is the sinusoidal component of the narrow-band reference signal, xbi(n)＝sin(ωin)，ωiAngular frequency that is a narrowband component in the reference signal;
wideband reference signal xB(n) is:
xB(n)＝x(n)-ys(n)。
step two, carrying out nonlinear expansion on the broadband reference signal through a FLANN filter in the broadband active noise reduction subsystem to obtain a first broadband output signal, carrying out discrete wavelet transformation on the first broadband output signal to obtain a second broadband output signal, and inputting the second broadband output signal into a broadband feedforward filter to obtain a third broadband output signal, namely a final output signal of the broadband subsystem; the method comprises the following specific steps:
21) the wideband reference signal xB(n) the first wideband output signal extended by the FLANN nonlinear filter is:
HB(n)
＝[xB(N)sin(πxB(n))cos(πxB(n))…sin(AπxB(n))cos(AπxB(n))…x(n
-1)sin(πxB(n-1))cos(πxB(n
-1))…sin(AπxB(n-1))cos(AπxB(n-1))…xB(n-N
+1)sin(πxB(n-N+1))cos(πxB(n-N
+1))…sin(AπxB(n-N+1))cos(AπxB(n-N+1))]
in the formula, xB(n) is a wideband reference signal; a is the order of the broadband active noise reduction subsystem reference signal expanded by the FLANN function; n is the length of the feedforward filter;
22) said first broadband output signal HB(n) performing a discrete wavelet transform to obtain:
Figure BDA0003249396250000093
in the formula, Ψj,k(n) is a discretized wavelet function;
Figure BDA0003249396250000094
j is a discrete scale factor; k is a discrete shift factor; z is a rational number set; n is the length of the feedforward filter; Ψ (2)-jn-k) a wavelet function;
the second broadband output signal after discrete wavelet transform reconstruction is:
Figure BDA0003249396250000101
wherein j is a discrete scale factor; k is a discrete shift factor; w (2)-j,2-jk) Is a discrete wavelet coefficient; Ψ (2)-jn-k) is a wavelet function;
23) the final output signal of the wide-band subsystem obtained by inputting the second wide-band output signal into the wide-band feedforward filter is as follows:
Figure BDA0003249396250000102
wherein n is a time index; w is ai(n) is the filter weight coefficient of the broadband active noise reduction subsystem; u. ofi(n) is a signal obtained by expanding a reference signal of the broadband active noise reduction subsystem; p is the order of the broadband active noise reduction subsystem reference signal expanded by the FLANN function; k is the number of layers of the signal after function expansion after discrete wavelet transform; i is the signal order after discrete wavelet transform; (2P +1) (k +1) is the number of frequency bands obtained by the input signals of the broadband active noise reduction subsystem after FLANN function expansion and discrete wavelet transformation.
Step three, carrying out nonlinear expansion on a narrow-band reference signal through a FLANN filter in a narrow-band active noise reduction subsystem to obtain a first narrow-band output signal, and inputting the first narrow-band output signal into a narrow-band feedforward filter to obtain a second narrow-band output signal, namely a final output signal of the narrow-band subsystem; the method comprises the following specific steps:
31) the narrowband reference signal ys(n) the first narrowband output signal extended by the FLANN nonlinear filter is:
Hai(n)
＝[xai(n)sin(πxai(n))cos(πxai(n))…sin(Pπxai(n))cos(Pπxai(n))…xai(n
-1)sin(πxai(n-1))cos(πxai(n
-1))…sin(Pπxai(n-1))cos(Pπxai(n-1))…xai(n-N
+1)sin(πxai(n-N+1))cos(πxai(n-N
+1))…sin(Pπxai(n-N+1))cos(Pπxai(n-N+1))]
Hbi
＝[xbi(n)sin(πxbi(n))cos(πxbi(n))…sin(Pπxbi(n))cos(Pπxbi(n))…xbi(n
-1)sin(πxbi(n-1))cos(πxbi(n
-1))…sin(Pπxbi(n-1))cos(Pπxbi(n-1))…xbi(n-N
+1)sin(πxbi(n-N+1))cos(πxbi(n-N
+1))…sin(Pπxbi(n-N+1))cos(Pπxbi(n-N+1))]
in the formula, Hai(n) is a narrowband reference signal cosine component FLANN extension; hbiCarrying out FLANN expansion on a narrow-band reference signal sinusoidal component; x is the number ofai(n) is the narrowband reference signal cosine component; x is the number ofbi(n) is the narrowband reference signal sinusoidal component; p is the order of the narrow-band signal expanded by the FLANN function; n is the length of the feedforward filter;
32) the final output signal of the narrowband subsystem obtained by inputting the first narrowband outgoing signal into the narrowband feedforward filter is as follows:
Figure BDA0003249396250000111
wherein n is a time index;
Figure BDA0003249396250000112
the filter weight coefficients of the n moments narrow-band active noise reduction subsystem are respectively; x is the number ofNai(n) is a signal of a reference signal cosine component of the narrow-band active noise reduction subsystem at the moment n after FLANN expansion; x is the number ofNai(n) is a signal of a sinusoidal component of a reference signal of the narrowband active noise reduction subsystem at n moments after FLANN expansion; q is the number of angular frequencies of the narrow-band component; and P is the order of the narrowband signal after being extended by the FLANN function.
Step four, summing the final output signal of the wide-band subsystem obtained in the step two and the final output signal of the narrow-band subsystem obtained in the step three to obtain an output signal of the nonlinear hybrid active noise control system; the method comprises the following specific steps:
y(n)＝yB(n)+yN(n)
in the formula, yB(n) is the final output signal of the broadband subsystem; y isNAnd (n) is a narrow-band output signal.
And step five, updating the weight coefficient of the feedforward filter in the broadband active noise reduction subsystem by adopting an M-max selector, updating the weight coefficient of the feedforward filter in the narrowband active noise reduction subsystem by adopting an FELMS algorithm, simplifying the weight coefficient, and reducing the calculation amount in the updating process, thereby obtaining the optimal output signal of the nonlinear hybrid active noise control system. The method comprises the following specific steps:
updating the weight coefficient of a filter in the broadband active noise reduction subsystem by adopting an M-max selector, and realizing the following steps:
wi(n+1)＝wi(n)+μBe(n)mi(n)
in the formula, wi(n) is the weight coefficient of the filter of the broadband active noise reduction subsystem; i is the order of the broadband signal; mu.sBStep size factor of the broadband active noise reduction subsystem; e (n) is the total error signal of the system; m isi(n) is the filtered wideband reference signal after selection by the M-max selector;
updating the weight coefficient of a filter in the narrow-band active noise reduction subsystem by using an FELMS algorithm, and realizing the following steps:
Figure BDA0003249396250000121
Figure BDA0003249396250000122
in the formula (I), the compound is shown in the specification,
Figure BDA0003249396250000123
the filter weight coefficients of the n moments narrow-band active noise reduction subsystem are respectively; mu.sNStep size factor for the narrowband active noise reduction subsystem;
Figure BDA0003249396250000124
to estimate the secondary acoustic path length; e.g. of the typef(n) is the filtered error signal;
Figure BDA0003249396250000125
Figure BDA0003249396250000129
and
Figure BDA0003249396250000126
to be delayed
Figure BDA0003249396250000127
Counting the number of narrowband reference signals;
Figure BDA0003249396250000128
to estimate a secondary acoustic path; j is a discrete scale factor;
the total error signal e (n) is:
e(n)＝d(n)-y′(n)
wherein d (n) is a nonlinear primary acoustic channel model with a relationship between output and reference signal input of d (n) ═ x (n) +0.8x (n-1) +0.3x (n-2) +0.4x (n-3) -0.8x (n) x (n-1) +0.9x (n) x (n-2) +0.7x (n) x (n-3) -3.9x (n-2) + n)2(n-1)x(n-2)-2.6x2(n- 1)x(n-3)+2.1x2(n-2) x (n-3), y '(n) is the output signal after the total output signal y (n) has passed through the secondary path, y' (n) ═ y (n) × s (n), and s (n) is the secondary acoustic path.
The above processes are repeated continuously, so that the effective noise reduction of the wide-band and narrow-band mixed signals in the nonlinear environment can be realized.
A nonlinear hybrid active noise control system is used for realizing a nonlinear hybrid active noise control method and comprises a signal separation subsystem, a narrow-band active noise reduction subsystem, a broadband active noise reduction subsystem, a computing system and an updating system;
the signal separation subsystem is used for separating a narrowband reference signal and a wideband reference signal from a mixed reference signal; the feedforward filter comprises a first feedforward filter submodule and a first weighted value updating submodule.
The first feedforward filter submodule is used for performing feedforward filtering on the mixed reference signal;
the first and second weight updating submodule is used for updating the weight coefficient of the feedforward filter of the signal separation subsystem;
the broadband active noise reduction subsystem is used for expanding and filtering a broadband reference signal to obtain a broadband output signal; the system comprises a first FLANN submodule, a first discrete wavelet transform submodule, a second feedforward filter submodule and a second weight updating submodule.
The first FLANN submodule is used for carrying out nonlinear expansion on a broadband reference signal;
the first discrete wavelet transform sub-module is used for performing discrete wavelet transform on the signal subjected to the nonlinear expansion;
the second feedforward filter submodule is used for performing feedforward filtering on the expanded wide-band subsystem signal;
the second weight updating submodule is used for updating the weight coefficient of the feedforward filter of the broadband subsystem;
the narrowband active noise reduction subsystem is used for expanding and filtering a narrowband reference signal to obtain a narrowband output signal; the second FLANN sub-module, the third feedforward filter sub-module and the third weight value updating sub-module are included.
The second FLANN submodule is used for carrying out nonlinear extension on the narrow-band reference signal;
the third feedforward filter submodule is used for performing feedforward filtering on the expanded narrowband subsystem signal;
the third weight updating submodule is used for updating the weight coefficient of the feedforward filter of the narrowband subsystem;
the computing system is used for summing the broadband output signal and the narrowband output signal to obtain an output signal of the nonlinear hybrid active noise control system;
the updating system is used for updating the weight coefficient of the feedforward filter in the broadband active noise reduction subsystem and the weight coefficient of the feedforward filter in the narrowband active noise reduction subsystem.
Examples
The comparison test of the nonlinear hybrid active noise control method provided by the invention and a plurality of typical active noise control systems in the prior art is as follows:
according to the noise characteristics of common industrial rotating machinery, a reference signal combined with a wide band and a narrow band of an active noise control system is synthesized, the narrow band noise is a sinusoidal noise signal superposed by 100Hz, 200Hz and 300Hz, the broadband noise is white Gaussian noise with the bandwidth limited to 100-1000 Hz, and the broadband noise is pink noise and Henon noise with the bandwidth limited to 100-1000 Hz, and the narrow band noise and the three kinds of broadband noise are superposed to form a wide-band and narrow-band mixed noise signal. In experiments, p (z) and s (z) represent the primary path transfer function and the secondary path transfer function, respectively, where the primary acoustic path employs a nonlinear model with a relationship between input and output: d (n) ═ x (n) +0.8x (n-1) +0.3x (n-2) +0.4x (n-3) -0.8x (n) x (n-1) +0.9x (n) x (n-2) +0.7x (n) x (n-3) -3.9x (n-2) +0.7x (n)2(n-1)x(n-2)-2.6x2(n- 1)x(n-3)+2.1x2(n-2) x (n-3), the secondary acoustic path is a linear model with amplitude-frequency and phase-frequency response curves as shown in fig. 4a and 4 b.
In order to fully check the effectiveness of the algorithm provided by the invention, a classical nonlinear active noise control algorithm comprising a filtering s-least mean square (FSLMS) algorithm and a mixed function linked artificial neural network (HFLANN) algorithm is selected for comparison test, by comparing the two algorithms with the modified function-linked artificial neural network (IHFLANN) algorithm and the nonlinear hybrid active noise control (SIHFLANN) algorithm, which are proposed in the present invention, the FSLMS algorithm HFLANN algorithm is a common nonlinear active noise control algorithm, and the IHFLANN algorithm is shown in fig. 2, adding a FLANN nonlinear filter and a discrete wavelet transform structure into a broadband active noise reduction subsystem of the HFLANN algorithm, the FLANN nonlinear filter is put into a narrow-band active noise reduction subsystem, the SIHFLANN algorithm is a nonlinear hybrid active noise control algorithm provided by the invention, an M-max selector and a FELMS algorithm are added on the basis of the IHFLANN algorithm. The test results of each algorithm are shown in fig. 5-7, and step-size factors selected by each algorithm in the test are shown in table 1 in order to ensure the fairness of algorithm comparison. The present invention uses an Average Noise Reduction (ANR) to evaluate the differences between algorithms. AverageThe expression formula of the noise reduction amount is as follows:
Figure BDA0003249396250000151
wherein A ise(n) is a recursive estimation of e (n), Ad(n) is a recursive estimate of d (n) expressed as
Figure BDA0003249396250000152
Wherein eta is 0.999, Ae(0)＝0，Ad(0)＝0。
TABLE 1 Experimental Algorithm step-size factor
Figure BDA0003249396250000153
As shown in fig. 5, the reference signal employs a mixture of complex sinusoidal noise and white gaussian noise. The composite sinusoidal noise adopts superposed signals of 100Hz, 200Hz and 300Hz, and the bandwidth of Gaussian white noise is limited to 100-1000 Hz. FIG. 5 shows a comparison of the noise attenuation performance of a reference noise signal using the FSLMS, HFLANN, IHFLANN, and SIHFLANN systems. As shown in fig. 5, the FSLMS algorithm has the worst performance of suppressing the mixed noise, the HFLANN system has performance similar to the FSLMS algorithm, and the ANR result at the final stage of the iteration is about-1.3 dB. The IHFLANN system performs best with ANR results of approximately-5.6 dB at steady state. The computation complexity of the SIHFLANN system is less than that of the IHFLANN system, but at the cost of poorer steady-state performance and lower convergence speed, and the ANR result is about-5 dB, which is nearly 0.6 dB higher than that of the IHFLANN system. In summary, (1) the IHFLANN system proposed by the present invention is effective in solving the above-mentioned mixed noise, and (2) the SIHFLANN system is less computationally complex than the IHFLANN system, and the attenuation performance is slightly worse than the IHFLLANN system.
As shown in fig. 6, the reference signal employs a mixture of complex sinusoidal and pink noise. The composite sinusoidal noise adopts superimposed signals of 100Hz, 200Hz and 300Hz, the bandwidth of the powder noise is limited to 100-1000 Hz, as shown in fig. 6, the FSLMS and HFLANN systems have similar attenuation performance when suppressing the reference noise, and the ANR results are about-1.0 dB and-1.5 dB, respectively. The IHFLANN system also has the best performance with ANR results of almost-5.5 dB. The SIHFLANN system performs slightly worse than the IHFLANN system, with an ANR result of almost-4.6 dB at the end of the iteration, approximately 0.9dB higher than the IHFLANN system, although the steady state performance is better than the FSLMS and HFLANN systems. It can be concluded that (1) the proposed IHFLANN and SIHFLANN systems have significant optimization compared to existing systems and (2) the SIHFLANN system has similar attenuation performance as the IHFLANN system, while the computation is reduced compared to the IHFLANN system.
As shown in fig. 7, the reference signal employs a mixture of complex sinusoidal and pink noise. The narrow-band signal is still a composite sinusoidal noise signal with the frequency of 100Hz, 200Hz and 300Hz, the broadband noise applies Henon chaotic noise, and the expression of the Henon chaotic noise can be written as follows: x (n) 1-ax2(n-1) + bx (n-2), the present invention sets the initial parameters of the Henon chaotic noise to x (0) ═ 0.1, x (1) ═ 0.1, a ═ 1.4, and b ═ 0.3. The performance of the FSLMS, HFLANN, IHFLANN and SIHFLANN systems is compared in FIG. 7. In FIG. 7, the performance of the FSLMS system is similar to the HFLANN system, with an ANR result of almost-2.7 dB. The IHFLANN system generally has better performance than the SIHFLANN system, with the ANR results of the IHFLANN system being almost-3.7 dB at the end of the iteration, around 0.3dB lower than the SIHFLANN system. It can be concluded that (1) the proposed algorithm has less difference in attenuation performance from the existing algorithms, and (2) the SIHFLANN system has similar attenuation performance to the IHFLANN system throughout the iteration, which means that the SIHFLANN system reduces the amount of computation without sacrificing attenuation performance.
As can be seen from the above three figures, the proposed system has better noise reduction performance than the existing system in a non-linear environment. Furthermore, the proposed SIHFLANN system, which applies the femms algorithm and the M-max selector to the IHFLANN system to reduce the computational complexity, has a noise reduction performance similar to that of the IHFLANN system. Numerical simulations show that the system proposed by the invention can improve the noise attenuation performance compared to the existing systems. Based on the analysis of the present invention, it can be concluded that the proposed system has a stronger ability to suppress mixed noise in a non-linear environment.

Claims (8)

1. A nonlinear hybrid active noise control method is characterized by comprising the following steps:
step one, acquiring a mixed reference signal required by a system, and separating a narrowband reference signal and a broadband reference signal in the mixed reference signal through a signal separation subsystem;
step two, carrying out nonlinear expansion on the broadband reference signal through a FLANN filter in the broadband active noise reduction subsystem to obtain a first broadband output signal, carrying out discrete wavelet transformation on the first broadband output signal to obtain a second broadband output signal, and inputting the second broadband output signal into a broadband feedforward filter to obtain a third broadband output signal, namely a final output signal of the broadband subsystem;
step three, carrying out nonlinear expansion on a narrow-band reference signal through a FLANN filter in a narrow-band active noise reduction subsystem to obtain a first narrow-band output signal, and inputting the first narrow-band output signal into a narrow-band feedforward filter to obtain a second narrow-band output signal, namely a final output signal of the narrow-band subsystem;
step four, summing the final output signal of the wide-band subsystem obtained in the step two and the final output signal of the narrow-band subsystem obtained in the step three through a computing system to obtain an output signal of the nonlinear hybrid active noise control system;
and step five, updating the weight coefficient of the feedforward filter in the broadband active noise reduction subsystem by the updating system by adopting an M-max selector, updating the weight coefficient of the feedforward filter in the narrowband active noise reduction subsystem by adopting an FELMS algorithm, and simplifying the weight coefficient so as to obtain the optimal output signal of the nonlinear hybrid active noise control system.
2. The nonlinear hybrid active noise control method according to claim 1, wherein the specific method of the first step is as follows:
the obtained mixed reference signal is x (n), and the narrow-band reference signal is ys(n) the broadband reference signal is xB(n); wherein, the narrowband reference signal ys(n) is:
Figure FDA0003249396240000011
in the formula, Q is the number of narrow-band frequencies;
Figure FDA0003249396240000012
and
Figure FDA0003249396240000013
discrete fourier coefficients for the signal separation subsystem; x is the number ofai(n) is the cosine component of the narrowband reference signal, xai(n)＝cos(ωin)，ωiAngular frequency that is a narrowband component in the reference signal; x is the number ofbi(n) is the sinusoidal component of the narrow-band reference signal, xbi(n)＝sin(ωin)，ωiAngular frequency that is a narrowband component in the reference signal;
wideband reference signal xB(n) is:
xB(n)＝x(n)-ys(n)。
3. the nonlinear hybrid active noise control method according to claim 1, wherein the specific method of the second step is as follows:
21) the wideband reference signal xB(n) the first wideband output signal extended by the FLANN nonlinear filter is:
HB(n)
＝[xB(n)sin(πxB(n))cos(πxB(n))…sin(AπxB(n))cos(AπxB(n))…x(n-1)sin(πxB(n-1))cos(πxB(n-1))…sin(AπxB(n-1))cos(AπxB(n-1))…xB(n-N+1)sin(πxB(n-N+1))cos(πxB(n-N+1))…sin(AπxB(n-N+1))cos(AπxB(n-N+1))]
in the formula, xB(n) is a wideband reference signal; a is the order of the broadband active noise reduction subsystem reference signal expanded by the FLANN function; n is the length of the feedforward filter;
22) said first broadband output signal HB(n) performing a discrete wavelet transform to obtain:
Figure FDA0003249396240000021
in the formula, Ψj，k(n) is a discretized wavelet function;
Figure FDA0003249396240000022
j is a discrete scale factor; k is a discrete shift factor; z is a rational number set; n is the length of the feedforward filter; Ψ (2)-jn-k) a wavelet function;
the second broadband output signal after discrete wavelet transform reconstruction is:
Figure FDA0003249396240000023
wherein j is a discrete scale factor; k is a discrete shift factor; w (2)-j，2-jk) Is a discrete wavelet coefficient; Ψ (2)-jn-k) is a wavelet function;
23) the final output signal of the wide-band subsystem obtained by inputting the second wide-band output signal into the wide-band feedforward filter is as follows:
Figure FDA0003249396240000031
wherein n is a time index; w is ai(n) is the filter weight coefficient of the broadband active noise reduction subsystem; u. ofi(n) is a signal obtained by expanding a reference signal of the broadband active noise reduction subsystem; p is the order of the broadband active noise reduction subsystem reference signal expanded by the FLANN function; k is the number of layers of the signal after function expansion after discrete wavelet transform; i is the signal order after discrete wavelet transform; (2P +1) (k +1) is obtained by FLANN function expansion and discrete wavelet transformation of input signals of the broadband active noise reduction subsystemThe number of frequency bands.
4. The nonlinear hybrid active noise control method according to claim 3, wherein the specific method of the third step is as follows:
31) the narrowband reference signal ys(n) the first narrowband output signal extended by the FLANN nonlinear filter is:
Hai(n)
＝[xai(n)sin(πxai(n))cos(πxai(n))…sin(Pπxai(n))cos(Pπxai(n))…xai(n-1)sin(πxai(n-1))cos(πxai(n-1))…sin(Pπxai(n-1))cos(Pπxai(n-1))…xai(n-N+1)sin(πxai(n-N+1))cos(πxai(n-N+1))…sin(Pπxai(n-N+1))cos(Pπxai(n-N+1))]
Hbi
＝[xbi(n)sin(πxbi(n))cos(πxbi(n))…sin(Pπxbi(n))cos(Pπxbi(n))…xbi(n-1)sin(πxbi(n-1))cos(πxbi(n-1))…sin(Pπxbi(n-1))cos(Pπxbi(n-1))…xbi(n-N+1)sin(πxbi(n-N+1))cos(πxbi(n-N+1))…sin(Pπxbi(n-N+1))cos(Pπxbi(n-N+1))]
in the formula, Hai(n) is a narrowband reference signal cosine component FLANN extension; hbiCarrying out FLANN expansion on a narrow-band reference signal sinusoidal component; x is the number ofai(n) is the narrowband reference signal cosine component; x is the number ofbi(n) is the narrowband reference signal sinusoidal component; p is the order of the narrow-band signal expanded by the FLANN function; n is the length of the feedforward filter;
32) the final output signal of the narrowband subsystem obtained by inputting the first narrowband outgoing signal into the narrowband feedforward filter is as follows:
Figure FDA0003249396240000041
wherein n is a time index;
Figure FDA0003249396240000042
the filter weight coefficients of the n moments narrow-band active noise reduction subsystem are respectively; x is the number ofNai(n) is a signal of a reference signal cosine component of the narrow-band active noise reduction subsystem at the moment n after FLANN expansion; x is the number ofNbi(n) is a signal of a sinusoidal component of a reference signal of the narrowband active noise reduction subsystem at n moments after FLANN expansion; q is the number of angular frequencies of the narrow-band component; and P is the order of the narrowband signal after being extended by the FLANN function.
5. The method as claimed in claim 4, wherein the output signal of the nonlinear hybrid active noise control system in the fourth step is specifically:
y(n)＝yB(n)+yN(n)
in the formula, yB(n) is the final output signal of the broadband subsystem; y isNAnd (n) is a narrow-band output signal.
6. The nonlinear hybrid active noise control method according to claim 5, wherein the specific method of the step five is:
updating the weight coefficient of a filter in the broadband active noise reduction subsystem by adopting an M-max selector, and realizing the following steps:
wi(n+1)＝wi(n)+μBe(n)mi(n)
in the formula, wi(n) is the weight coefficient of the filter of the broadband active noise reduction subsystem; i is the order of the broadband signal; mu.sBStep size factor of the broadband active noise reduction subsystem; e (n) is the total error signal of the system; m isi(n) is the filtered wideband reference signal after selection by the M-max selector;
updating the weight coefficient of a filter in the narrow-band active noise reduction subsystem by using an FELMS algorithm, and realizing the following steps:
Figure FDA0003249396240000051
Figure FDA0003249396240000052
in the formula (I), the compound is shown in the specification,
Figure FDA0003249396240000053
the filter weight coefficients of the n moments narrow-band active noise reduction subsystem are respectively; mu.sNStep size factor for the narrowband active noise reduction subsystem;
Figure FDA0003249396240000054
to estimate the secondary acoustic path length; e.g. of the typef(n) is the filtered error signal;
Figure FDA0003249396240000055
Figure FDA0003249396240000056
and
Figure FDA0003249396240000057
to be delayed
Figure FDA0003249396240000058
Counting the number of narrowband reference signals;
Figure FDA0003249396240000059
to estimate the secondary acoustic path.
7. The nonlinear hybrid active noise control method according to claim 6,
the total error signal e (n) is:
e(n)＝d(n)-y′(n)
wherein d (n) is a non-linearA sexual primary sound channel model having an output in relation to a reference signal input of d (n) ═ x (n) +0.8x (n-1) +0.3x (n-2) +0.4x (n-3) -0.8x (n) x (n-1) +0.9x (n) x (n-2) +0.7x (n) x (n-3) -3.9x (n-3) × n2(n-1)x(n-2)-2.6x2(n-1)x(n-3)+2.1x2(n-2) x (n-3), y '(n) is the output signal after the total output signal y (n) has passed through the secondary path, y' (n) ═ y (n) × s (n), and s (n) is the secondary acoustic path.
8. A nonlinear hybrid active noise control system is used for realizing a nonlinear hybrid active noise control method and is characterized by comprising a signal separation subsystem, a narrow-band active noise reduction subsystem, a broadband active noise reduction subsystem, a computing system and an updating system;
the signal separation subsystem is used for separating a narrowband reference signal and a wideband reference signal from a mixed reference signal;
the broadband active noise reduction subsystem is used for expanding and filtering a broadband reference signal to obtain a broadband output signal;
the narrowband active noise reduction subsystem is used for expanding and filtering a narrowband reference signal to obtain a narrowband output signal;
the computing system is used for summing the broadband output signal and the narrowband output signal to obtain an output signal of the nonlinear hybrid active noise control system;
the updating system is used for updating the weight coefficient of the feedforward filter in the broadband active noise reduction subsystem and the weight coefficient of the feedforward filter in the narrowband active noise reduction subsystem.
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